Bryan Robson, whose promotion favourites were on a nine-match unbeaten run, was helpless as his defenders fell apart to hand Tony Pulis' side a 3-0 lead half-time lead.
The Sheffield side, who won 1-0 at the Britannia Stadium three weeks ago, were shell-shocked when Stoke took the lead on two minutes after a simple three-man move.
Ryan Shawcross' free-kick found the unmarked Liam Lawrence lurking at the far post, and the midfielder picked out ex-Sheffield Wednesday striker Richard Cresswell who shot past the exposed Paddy Kenny from six yards.
Robson's side were in trouble five minutes later after another embarrassing blunder saw Stoke surge further ahead.
Lawrence strode up to take a free-kick from the left flank, curling the ball towards the far post as the Blades' leading scorer James Beattie tried to clear only to bundle the ball over the line.
United's fragile back four crumbled again on 19 minutes with Lawrence again the provider. His curling free-kick from the right produced a close-range header from Cresswell, the ball hitting Shawcross and spinning past the helpless Kenny.
Robson, who had demanded an improved home performance to pacify the fans because of his side's poor record at Bramall Lane, brought off midfielder Nick Montgomery for the lanky Jon Stead on 23 minutes to join lone striker Beattie but there was no way back.
Kenny produced a stunning save, diving quickly to block Ricardo Fuller's effort as the Jamaica international conjured up a moment of magic in the area, before drilling in a low 15-yard shot as impressive Stoke pushed for a fourth goal.
Steve Simonsen produced his first save in the 70th minute after full-back Phil Bardsley had threaded the ball to Michael Tonge. The United midfielder took a stride before firing in a right-foot effort that was blocked by the diving keeper.